14 FLUIDITY AND PLASTICITY
a very careful study of the earlier work on viscosity and gave a
theoretical derivation of the law of Poiseuille, which has had
very great effect upon the succeeding history of this subject.
Neumann gave the deduction of the Law of Poiseuille in his
lectures on Hydrodynamics in 1858, and thus prior to the publi-
cation of Hagenbach's paper in March, 1860. This deduction
was first published by Jacobson early in 1860 and the lectures
! were published in full in 1883. In April, 1860 Helmholtz pub-
I lished the derivation of the law from the equations of motion.
| J. Stephan (1862) and Mathieu (1863) gave independent deriva-
| tions of the law. Reference should also be made to the treat-
jl' ment of the flow in long narrow tubes by Stokes (1849).
I Imagine a horizontal capillary whose bore is a true cylinder to
I connect two reservoirs L (left) and R (right) there being a differ-
, j; ence of pressure between the two reservoirs, at the level of the
| capillary, amounting to p grams per square centimeter. If the pres-
il sure in L is the greater the direction of flow through the capillary
! I will be from left to right. The total effective pressure p is used
,' 7 up in doing various forms of work, several of which can be differ-
<j entiated with a resultant gain in clearness of understanding of
), the conditions of flow.
f. 1. Near the entrance to the capillary the particles of fluid
undergo a rapid acceleration; this absorption of kinetic energy
causes a fall in the pressure amounting to pk.
\ 2. Within the capillary, there may be a finite movement of
the fluid over the walls of the tube, due to slipping. Unless
the external friction is zero or infinity, work will be done and
there will be a fall of pressure pa.
3. Unless the external friction is zero, the layers of fluid
nearer the walls of the tube will move more slowly than the
f! layers nearer the axis of the tube, and an absorption of pressure
. due to this internal friction will result. Let this be pv.
, 4. If the path of the particles through the capillary is not
f perfectly linear, the additional distance travelled in the eddies,
, will give rise to a further drop in the pressure amounting to pe*
This turbulent flow is certain to occur when the velocity of flow
|| becomes sufficiently high.
!j 5. But even before the velocity becomes turbulent it seems
fi possible that the stream lines at the extremities of the tube may